Without giving it much thought, I've always roasted garlic for use in cooked preparations (hummus, spaghetti sauce, garlic bread, etc.), and used it raw for uncooked preparations (salad dressings, tzatziki sauce, etc.).

Cooking with friends recently, one said all that matters is how much or little garlic pungency you want in that dish; another said the acidity of the other ingredients in the recipe dictate which form tastes best (raw with tart or acidic flavors; roasted with more salty and savory flavors).

Of course, personal taste preferences will nearly always trump cooking traditions and rules of thumb, but is there science or logic behind choosing which form for a particular dish?
Other than roasted garlic being milder and sweeter than raw, does either go with a particular cooking method or set of ingredients better than the other?

I find this question odd, because you seem to operate on the presumption that roasting is the only way to cook garlic. You also need to consider the much more common method of sauteeing it, and the effects of chopping it to various degrees (i.e. the finer you chop it, the stronger the taste).
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ElendilTheTallDec 2 '12 at 14:44

I don't think any "right" answer is possible for this question; it's strictly a matter of personal taste.
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FuzzyChefDec 6 '12 at 6:28

4 Answers
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As covered on wikipedia, raw garlic has a number of sulfur-containing compounds, among them allicin, which are responsible for the burning feeling raw garlic imparts to a dish. When cooked into food, these flavors mellow and the compounds are boiled off or denatured. Other enzymatic and non-enzymatic transformative and browning processes also take place as garlic is cooked.

Roasting garlic produces these changes in garlic before-hand, and in a more controlled way. As the garlic heats up and starts browning, the raw garlic character is lost, while sweetness from melanoidin (a product of the reaction of amino acids with sugar, per the Maillard reaction) and savoryness (from the denaturing, concentrating amino acid content) are gained. The extreme example of this is Black Garlic (discussed at some length on my blog), in which the sweet and savory content of the garlic has been processed and concentrated over the course of a month, with the flavor resembling non-sour Balsamic vinegar.

With that said, the inclusion of raw or pre-processed garlic will depend on the proportions of the two above-noted sets of flavors that are desired in a dish. If added raw to uncooked food, it will add very little savory or sweet, and plenty of aroma and burn. If added roasted to that same food, it will add mostly savory and sweet, with very little of the burn. Any further cooking that takes place after garlic's addition to a recipe will further discourage the raw flavors and aromas.

It's actually pretty simple: as you put it, roasted garlic is milder and sweeter. So if you're looking for a sweeter, milder garlic taste, you'll want to use roasted garlic. Applications such as 40 Clove Chicken, where garlic is the primary flavoring agent, tend to use cooked whole cloves to avoid overpowering the dish with sharp tastes. (Whole cloves are also less strong than smaller pieces of cloves, in general).

Onion is much the same way; if you want a sharp bite to your dish, you'll keep the onions as uncooked as possible, whereas a more subtle flavor can be had from cooked onions. For a good example, try a burger with chopped but raw onions as opposed to a burger with sauteed onions.

Basically, you pick the cooking method of the garlic based on what flavor profile you want the dish to have.

The reasons that garlic is used whole in some applications such as the 40 clove chicken mentioned above are not only to keep the garlic from overcooking but because when you cut into an allium such as garlic or onions you mix chemicals inside the garlic that react with each other. Garlic will be much milder cooked whole than in pieces.
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FladaboscoDec 16 '12 at 15:55

I would think that science has little to do with it but rather more a matter of texture and aroma. Raw garlic is much more aromatic and "spicy" since it's natural aromatic compounds have not been altered by heat and it is also much more firm obviously since the cell walls are still generally intact and rigid. I find that approaching garlic is a lot like painting a wall, do you want it to shine through, accent, or blend in? Depending on how you answer that question it can range from raw, sauteed, roasted, fried, sliced thin, pureed, etc. But scientifically, I don't think that outside of shared aromatic compounds with certain foods the way it is used makes a difference.

You can also go to https://www.foodpairing.com/ and see how different foods pair together based upon shared flavor and aromatic compounds found in each.

Science? No Logic? Yes -what sort of flavor do I want/need? does it go? how much?. I play with garlic many different ways (shaved, chopped, minced and whole) and it does seem to find its way into most of my dinners. Rarely, however, do I roast it. If I do, it is usually for a stew, an herbed butter, or some sort of cheese board or orderves.